Question

By using section formula, show that the points $(-1,2)(2,5)$ and $(5,8)$ are collinear.

Answer 1

Given,

$A(-1,2),C(2,5),B(5,8)$

Let C divide the line AB in the ration, $k:1$

$\therefore (\frac{m{x}_2+n{x}_1}{m+n},\frac{m{y}_2+n{y}_1}{m+n})=(2,5)$

$(\frac{k\left(5\right)+1(-1)}{k+1},\frac{k\left(8\right)+1\left(2\right)}{k+1})=(2,5)$

$\frac{5k-1}{k+1}=2$.....(1)

$\frac{8k+2}{k+1}=5$......(2)

Solving equation (1), we get

$k=1$

$\Rightarrow C$ is the mid point of line $AB$

Hence given points are collinear.